/7x-15=2x-10

Solution for /7x-15=2x-10 equation:

/7x-15=2x-10

We move all terms to the left:

/7x-15-(2x-10)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

/7x-2x+10-15=0

We multiply all the terms by the denominator


-2x*7x+10*7x-15*7x+=0

We add all the numbers together, and all the variables

-2x*7x+10*7x-15*7x=0

Wy multiply elements

-14x^2+70x-105x=0

We add all the numbers together, and all the variables

-14x^2-35x=0

a = -14; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-14)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-14}=\frac{70}{-28}
=-2+1/2
$